E2 VoC Analyses Part 2: Regression Analyses

Participant info

Agency task: Agency decisions

Model: Agency decisions by VoC

## Mixed Model Anova Table (Type 3 tests, LRT-method)
## 
## Model: stage_1_choice ~ voc_z * condition_trial * age_z + (voc_z * condition_trial || 
## Model:     subject_id)
## Data: agency_model_data
## Df full model: 12
##                        Effect df      Chisq p.value
## 1                       voc_z  1 166.62 ***   <.001
## 2             condition_trial  1       0.07    .796
## 3                       age_z  1       0.00    .965
## 4       voc_z:condition_trial  1  51.94 ***   <.001
## 5                 voc_z:age_z  1  12.28 ***   <.001
## 6       condition_trial:age_z  1       0.01    .941
## 7 voc_z:condition_trial:age_z  1     5.26 *    .022
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: stage_1_choice ~ voc_z * condition_trial * age_z + (1 + re1.voc_z +  
##     re1.condition_trial + re1.voc_z_by_condition_trial || subject_id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+06))
## 
##      AIC      BIC   logLik deviance df.resid 
##  38797.4  38902.4 -19386.7  38773.4    46747 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -37.884  -0.383   0.172   0.500  37.176 
## 
## Random effects:
##  Groups       Name                         Variance Std.Dev.
##  subject_id   (Intercept)                  4.51651  2.1252  
##  subject_id.1 re1.voc_z                    0.49713  0.7051  
##  subject_id.2 re1.condition_trial          0.82459  0.9081  
##  subject_id.3 re1.voc_z_by_condition_trial 0.04873  0.2207  
## Number of obs: 46759, groups:  subject_id, 150
## 
## Fixed effects:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                  1.262232   0.175381   7.197 6.15e-13 ***
## voc_z                        1.094665   0.061065  17.926  < 2e-16 ***
## condition_trial             -0.020084   0.077009  -0.261 0.794244    
## age_z                        0.007827   0.174968   0.045 0.964321    
## voc_z:condition_trial        0.200551   0.025091   7.993 1.32e-15 ***
## voc_z:age_z                  0.218518   0.061013   3.581 0.000342 ***
## condition_trial:age_z       -0.005669   0.076840  -0.074 0.941189    
## voc_z:condition_trial:age_z  0.058323   0.025115   2.322 0.020219 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) voc_z  cndtn_ age_z  vc_z:c_ vc_z:g_ cnd_:_
## voc_z        0.012                                            
## conditn_trl  0.012  0.007                                     
## age_z        0.000  0.001 -0.002                              
## vc_z:cndtn_  0.006  0.043  0.034  0.001                       
## voc_z:age_z  0.002 -0.006  0.001  0.010 -0.001                
## cndtn_trl:_ -0.002  0.001 -0.009  0.007  0.005   0.004        
## vc_z:cnd_:_  0.001  0.000  0.005  0.003  0.000   0.036   0.033

Predictor	Log-Odds	SE	Statistic	p
intercept	1.26	0.18	7.20	<0.001
VoC	1.09	0.06	17.93	<0.001
trial	-0.02	0.08	-0.26	0.794
age	0.01	0.17	0.04	0.964
VoC x trial	0.20	0.03	7.99	<0.001
VoC x age	0.22	0.06	3.58	<0.001
trial x age	-0.01	0.08	-0.07	0.941
VoC x trial x age	0.06	0.03	2.32	0.020

Plot: Sensitivity to the value of choice

Plot: Sensitivity to value of choice with continuous age

Summary stats: Sensitivity to value of control

Agency decision reaction times

Model: Agency RTs by VoC

## Mixed Model Anova Table (Type 3 tests, S-method)
## 
## Model: agencyLogRT ~ zAge * zAbsVoC * zTrialOfCond + (zAbsVoC * zTrialOfCond | 
## Model:     subject_id)
## Data: banditTask.RT.data
##                      Effect         df         F p.value
## 1                      zAge  1, 147.99      0.63    .427
## 2                   zAbsVoC  1, 148.61 17.05 ***   <.001
## 3              zTrialOfCond  1, 147.97 71.56 ***   <.001
## 4              zAge:zAbsVoC  1, 148.39    4.43 *    .037
## 5         zAge:zTrialOfCond  1, 147.97      0.09    .767
## 6      zAbsVoC:zTrialOfCond 1, 1560.95      0.21    .647
## 7 zAge:zAbsVoC:zTrialOfCond 1, 1562.56      0.61    .435
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## agencyLogRT ~ zAge * zAbsVoC * zTrialOfCond + (zAbsVoC * zTrialOfCond |  
##     subject_id)
##    Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+06))
## 
## REML criterion at convergence: 62132.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.3588 -0.6227 -0.0891  0.5275  5.7413 
## 
## Random effects:
##  Groups     Name                 Variance  Std.Dev. Corr             
##  subject_id (Intercept)          1.213e-01 0.34823                   
##             zAbsVoC              2.648e-04 0.01627  -0.29            
##             zTrialOfCond         1.790e-02 0.13379   0.05  0.00      
##             zAbsVoC:zTrialOfCond 2.798e-05 0.00529  -0.70  0.52 -0.67
##  Residual                        2.147e-01 0.46336                   
## Number of obs: 46759, groups:  subject_id, 150
## 
## Fixed effects:
##                             Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)               -4.785e-02  2.851e-02  1.480e+02  -1.678   0.0954 .  
## zAge                      -2.269e-02  2.851e-02  1.480e+02  -0.796   0.4275    
## zAbsVoC                   -1.041e-02  2.521e-03  1.486e+02  -4.130 6.04e-05 ***
## zTrialOfCond              -9.417e-02  1.113e-02  1.480e+02  -8.459 2.39e-14 ***
## zAge:zAbsVoC              -5.307e-03  2.520e-03  1.484e+02  -2.106   0.0369 *  
## zAge:zTrialOfCond         -3.300e-03  1.113e-02  1.480e+02  -0.297   0.7673    
## zAbsVoC:zTrialOfCond      -1.000e-03  2.187e-03  1.561e+03  -0.457   0.6475    
## zAge:zAbsVoC:zTrialOfCond  1.709e-03  2.187e-03  1.563e+03   0.781   0.4346    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) zAge   zAbsVC zTrlOC zAg:AVC zA:TOC zAVC:T
## zAge         0.004                                           
## zAbsVoC     -0.154 -0.001                                    
## zTrialOfCnd  0.053  0.000 -0.001                             
## zAge:zAbsVC -0.001 -0.154  0.002  0.000                      
## zAg:zTrlOfC  0.000  0.053  0.000  0.004 -0.001               
## zAbsVC:zTOC -0.138  0.000  0.055 -0.129 -0.001   0.000       
## zAg:AVC:TOC  0.000 -0.138 -0.001  0.000  0.054  -0.129 -0.001
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

Predictor	Estimates	SE	p
intercept	-0.05	0.03	0.093
age	-0.02	0.03	0.426
VoC magnitude	-0.01	0.00	<0.001
trial	-0.09	0.01	<0.001
age x VoC magnitude	-0.01	0.00	0.035
age x trial	-0.00	0.01	0.767
VoC magnitude x trial	-0.00	0.00	0.647
age x VoC magnitude x trial	0.00	0.00	0.435

Plot: Agency RTs by VoC

Agency task: Machine selection

Model: Optimal machine choices across trials by condition and age

## Mixed Model Anova Table (Type 3 tests, LRT-method)
## 
## Model: stage_2_acc ~ context * condition_trial * age_z + (context * 
## Model:     condition_trial || subject_id)
## Data: machine_model_data
## Df full model: 12
##                          Effect df     Chisq p.value
## 1                       context  1 29.27 ***   <.001
## 2               condition_trial  1 69.50 ***   <.001
## 3                         age_z  1 15.49 ***   <.001
## 4       context:condition_trial  1    5.47 *    .019
## 5                 context:age_z  1      0.74    .389
## 6         condition_trial:age_z  1      0.70    .404
## 7 context:condition_trial:age_z  1      1.71    .191
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: stage_2_acc ~ context * condition_trial * age_z + (1 + re1.context1 +  
##     re1.condition_trial + re1.context1_by_condition_trial ||      subject_id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+06))
## 
##      AIC      BIC   logLik deviance df.resid 
##  15084.2  15179.9  -7530.1  15060.2    21318 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -10.7613   0.0972   0.2017   0.4001   2.4112 
## 
## Random effects:
##  Groups       Name                            Variance Std.Dev.
##  subject_id   (Intercept)                     1.7634   1.3279  
##  subject_id.1 re1.context1                    0.6000   0.7746  
##  subject_id.2 re1.condition_trial             0.2931   0.5414  
##  subject_id.3 re1.context1_by_condition_trial 0.1118   0.3344  
## Number of obs: 21330, groups:  subject_id, 149
## 
## Fixed effects:
##                                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                     2.31547    0.11532  20.078  < 2e-16 ***
## context1                        0.40971    0.07119   5.755 8.65e-09 ***
## condition_trial                 0.49629    0.05390   9.208  < 2e-16 ***
## age_z                           0.45938    0.11421   4.022 5.77e-05 ***
## context1:condition_trial        0.09387    0.03923   2.393   0.0167 *  
## context1:age_z                 -0.06268    0.07112  -0.881   0.3782    
## condition_trial:age_z           0.04491    0.05342   0.841   0.4006    
## context1:condition_trial:age_z -0.05214    0.03913  -1.333   0.1827    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) cntxt1 cndtn_ age_z  cntxt1:c_ cntxt1:g_ cnd_:_
## context1     0.033                                                
## conditn_trl  0.077  0.031                                         
## age_z        0.038  0.004  0.011                                  
## cntxt1:cnd_  0.028  0.108  0.077  0.000                           
## contxt1:g_z  0.000  0.054 -0.003  0.023  0.014                    
## cndtn_trl:_  0.007 -0.002  0.071  0.061  0.003     0.021          
## cntxt1:c_:_ -0.003  0.014  0.004  0.017  0.106     0.106     0.066

Predictor	Log-Odds	SE	Statistic	p
intercept	2.32	0.12	20.08	<0.001
condition	0.41	0.07	5.76	<0.001
trial	0.50	0.05	9.21	<0.001
age	0.46	0.11	4.02	<0.001
condition x trial	0.09	0.04	2.39	0.017
condition x age	-0.06	0.07	-0.88	0.378
trial x age	0.04	0.05	0.84	0.401
condition x trial x age	-0.05	0.04	-1.33	0.183

Plot: Proportion optimal machine selections across age groups and trials

Explicit reward knowledge task

Explicit reward knowledge task: summary stats

Model: Explicit reward knowledge by age and true probabilities

## Mixed Model Anova Table (Type 3 tests, S-method)
## 
## Model: error ~ zTrueProb * zAge + (1 | subject_id)
## Data: explicitKnow.filtered
##           Effect        df         F p.value
## 1      zTrueProb 1, 748.00 23.42 ***   <.001
## 2           zAge 1, 148.00   7.59 **    .007
## 3 zTrueProb:zAge 1, 748.00      0.52    .473
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: error ~ zTrueProb * zAge + (1 | subject_id)
##    Data: data
## 
## REML criterion at convergence: 3093.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5243 -0.7034 -0.1905  0.4417  4.1618 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_id (Intercept) 0.1159   0.3405  
##  Residual               1.6947   1.3018  
## Number of obs: 900, groups:  subject_id, 150
## 
## Fixed effects:
##                 Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)      1.58778    0.05154 148.00000  30.810  < 2e-16 ***
## zTrueProb       -0.21012    0.04342 747.99999  -4.840 1.58e-06 ***
## zAge            -0.14204    0.05156 148.00000  -2.755  0.00661 ** 
## zTrueProb:zAge  -0.03119    0.04344 747.99999  -0.718  0.47293    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) zTrPrb zAge 
## zTrueProb   0.000              
## zAge        0.000  0.000       
## zTruPrb:zAg 0.000  0.000  0.000

Plot: Explicit reward knowledge